1. Field of the Invention
This invention relates to tuning of resonator gyroscopes. Particularly, this invention relates to tuning of microelectromechanical system (MEMS) disc resonator gyroscopes.
2. Description of the Related Art
Most high-performance vibratory angular rate sensors rely on the matching of the frequencies of two modes that are highly coupled by a Coriolis acceleration term when the equations of motion are written in a case-fixed coordinate system. Frequency matching exploits the mechanical gain afforded by the sensor dynamics and leads to the best attainable signal-to-electronic noise ratio. The degenerate dynamics can be attained by designing structures with a high degree of symmetry and in the case of the Boeing Silicon disc resonator gyro (SiDRG), this symmetric design also provides a high degree of isolation of the Coriolis modes from linear acceleration of the sensor case. These ideas have also been exploited in Litton's hemispherical resonator gyro (HRG), the BAE nickel ring gyro, and the BEI quartz tuning fork gyro. In all of these sensors, the anchor attaching the resonant structure to the sensor case is, ideally, a nodal point for the Coriolis coupled modes and the symmetric design, on its face, guarantees degenerate modal frequencies. Furthermore, the high degree of isolation reduces energy dissipation in the modes, which is a source of angular rate bias and drift. The HRG is an extreme example of the degree of isolation that can be achieved; quality factors exceeding 6×106 have been reported when the resonators are fabricated from fused quartz. See, e.g. Loper et al., “The HRG. A new low-noise inertial rotation sensor,” 16th Joint Services Data Exchange for Inertial Systems, Los Angeles, Calif. November 1981; Lynch, “Hemispherical Resonator Gyro,” In Ragan. R. R. (ed.) “Inertial technology for the future,” IEEE Trans on Aerospace and Electronic Systems, AES-20, 4. pp. 414-444, 1984; which are both incorporated by reference herein.
FIG. 1 illustrates typical modal frequency splitting in a disc resonator gyroscope. The SiDRG frequency response is shown with a narrow, 100 Hz band encompassing the “fundamental” Coriolis modes. Though the frequency split is small in a relative sense (e.g. less than 0.3%), the sensor effectively has no mechanical gain in this state. For those sensors lending themselves to MEMS fabrication, such as the SiDRG, local variations in etch rate produce very small, but somewhat unpredictable, asymmetries that manifest themselves as such splitting of the modal frequencies. Although the frequency splits are small (e.g. on the order of 0.3% or less), the absolute separation between the modal frequencies coupled with their relatively high Q conspire to eliminate the mechanical gain advantage that was a primary objective of sensor's design in the first place.
In past work, the resonant frequencies of the SiDRG have been tuned by locally altering the resonator stiffness by applying electrostatic forces with dedicated electrodes See, e.g. Adam et al., “Independent Tuning of Linear and Nonlinear Stiffness Coefficients,” IEEE J. Microelectroomechanical Systems, Vol 7. No. 2. pp. 172-180, 1998; Ayazi et al., “A HARPS Polysilicon Vibrating Ring Gyroscope,” IEEE J Microelectromechanical Systems. Vol. 10, No. 2, pp. 169-179, 2001; and Kim et al. “A systematic method for tuning the dynamics of electrostatically actuated vibratory gyros,” IEEE Trans. Control System Technology, Vol. 14, No. 1, pp 69-81, 2006; which are all incorporated by reference herein. Unfortunately the electrodes are required to hold a very stable voltage over the operating environment, which can be difficult to do with compact, low-cost electronics. The possibility of tuning the modes by permanently altering the mass distribution of the sensor is attractive because it eliminates the need for tuning bias voltages. See, e.g., Ahddmoneum et al., “Location-Dependent Frequency Tuning of Vibrating Micromechanical Resonators Via Laser Trimming” 2004 IEEE lnt. Ultrasonics, Ferroelectrics, and Frequency Control. Symp., pp 272-279, 2004; which is incorporated by reference herein.
In view of the foregoing, there is a need in the art for techniques for efficiently tuning resonator gyroscopes. In addition, there is a need for such techniques to enhance overall performance of such gyroscopes at a reduced cost. There is further a need for such techniques for resonator gyroscopes in space applications. These and other needs are met by the teaching of the present disclosure as detailed hereafter.